Convert grain / liter to grain / barrel

Learn how to convert 1 grain / liter to grain / barrel step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a i n}{l i t e r}) = x (\frac{g r a i n}{b a r r e l})

Define the base values of the selected units in relation to the SI unit

(\frac{k i l o g r a m}{c u b i c m e t e r})

Left side: 1.0 (\frac{g r a i n}{l i t e r}) = 6.479891 \times 10^{- 2} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 6.479891 \times 10^{- 2} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{b a r r e l}) = \frac{6.479891 \times 10^{- 5}}{0.16365924} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 5}}{0.16365924} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{g r a i n}{l i t e r}) = x (\frac{g r a i n}{b a r r e l})

Insert known values =>

1.0 \times 6.479891 \times 10^{- 2} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{6.479891 \times 10^{- 5}}{0.16365924} \times (\frac{k i l o g r a m}{c u b i c m e t e r})

Or

1.0 \cdot 6.479891 \times 10^{- 2} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891 \times 10^{- 5}}{0.16365924} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times 6.479891 \times 10^{- 2} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891 \times 10^{- 5}}{0.16365924} \times (\frac{k g}{m^{3}})

Conversion Equation

6.479891 \times 10^{- 2} = x \times \frac{6.479891 \times 10^{- 5}}{0.16365924}

Cancel factors on both sides

Cancel factors

6.479891 \times 10^{- 2} = x \times \frac{6.479891 \times {10^{- 5}}^{10^{- 3}}}{0.16365924}

Simplify

1.0 = x \times \frac{10^{- 3}}{0.16365924}

Switch sides

x \times \frac{10^{- 3}}{0.16365924} = 1.0

Isolate

x

Multiply both sides by

(\frac{0.16365924}{10^{- 3}})

x \times \frac{10^{- 3}}{0.16365924} \times \frac{0.16365924}{10^{- 3}} = \times \frac{0.16365924}{10^{- 3}}

Cancel

x \times \frac{10^{- 3} \times 0.16365924}{0.16365924 \times 10^{- 3}} = \frac{0.16365924}{10^{- 3}}

Simplify

x = \frac{0.16365924}{10^{- 3}}

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

x = 10^{3} \times 0.16365924

Solve

x

x = 163.65924 \approx 1.6366 \times 10^{2}

Conversion Equation

1.0 (\frac{g r a i n}{l i t e r}) \approx 1.6366 \times 10^{2} (\frac{g r a i n}{b a r r e l})

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